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# In the rectangular coordinate system are the points (r, s)

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Joined: 14 Oct 2004
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In the rectangular coordinate system are the points (r, s) [#permalink]

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08 Dec 2004, 16:41
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In the rectangular coordinate system are the points (r, s) and ( u, v) equidistant from the origin?

1) r + s = 1

2) u = 1-r and v = 1 - s
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08 Dec 2004, 16:56
Pick C

Distance between two points = sqrt[(x2-x1)^2+(y2-y1)^2]

Distance between (0,0) and (r,s) = sqrt(r^2+s^2)
Distance between (0,0) and (u,v) = sqrt(u^2+v^2)

Stem: Is sqrt(r^2+s^2) = sqrt(u^2+v^2)? or Is r^2+s^2 = u^2+v^2 (since distance is always poistive)

s[1]: r+s = 1
Insufficient as we do not know anything about (u,v)

s[2]: u=1-r; v=1-s
u^2+v^2 = (1-r)^2 + (1-s)^2 = 2+r^2+s^2-2(r+s)
Is r+s = 1 then its true else its not.
Insufficient

s[1]+s[2]: u^2+v^2 = 2+r^2+s^2-2(r+s) = r^2+s^2
So sufficient.
08 Dec 2004, 16:56
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